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Homework Help: Transition Probability of Hydrogen atom in an electric field

  1. Dec 6, 2012 #1
    A hydrogen atom is in its ground state and is subject to an external electric field of

    E = ε([itex]\hat{x}[/itex]+[itex]\hat{y}[/itex]+2[itex]\hat{z}[/itex])e-t/[itex]\tau[/itex]

    I'm confused as to how to compute the matrix elements of the perturbed hamiltonian since this is not in the z direction.

    Would I have to do something like this?

    H'ba = -pE = -qεe-t/[itex]\tau[/itex]<[itex]\psi[/itex]b|([itex]\hat{x}[/itex]+[itex]\hat{y}[/itex]+2[itex]\hat{z}[/itex])|[itex]\psi[/itex]a>

  2. jcsd
  3. Dec 7, 2012 #2


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    If I remember this stuff correctly, then yes. You're just using a unit vector in the direction of the electric field rather than in the z direction. Alternatively, you could rotate your coordinate system so that the electric field points in the z direction, solve the problem, and then rotate your solution back to the original coordinates.
  4. Dec 7, 2012 #3


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    Shouldn't you take the dot product of the electric field with the dipole moment vector operator: ##\vec{p} = q\vec{r}= q(x \hat{x} + y \hat{y}+z \hat{z})##?
  5. Dec 7, 2012 #4


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    Oh yes, somehow I completely missed the fact that there was no dot product in the original post.
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